Lemma of the day

Let X be an algebraic space. Let x ∈ |X|. If X is separated, locally Noetherian, and the dimension of the local ring of X at x is ≤1 (Definition Tag 04NA), then there exists an open subspace of X containing x which is a scheme. See Lemma Tag 0ADD.

Slogan: Separated algebraic spaces are schemes in codimension 1.